Should trigonometric functions be cached?

Question

How extensive are functions like Math.sin(), Math.cos() etc.? Does the compiler optimise the code if you call the method with the same arguments multiple times in a row? If not, at how many calls of these methods should you start caching the result in a variable?

Answer 1

The trigonometric functions are usually implemented as Taylor expansions. They are fast. You can write your own and compare.

public class Main{
    private static double factorial(double n) {
        if (n <= 1) // base case
            return 1;
        else
            return n * factorial(n - 1);
    }
    private static double sin(int n) {
        int PRECISION = 10;
        double rad = n*1./180.*Math.PI;
        double sum = rad;
        for (int i = 1; i <= PRECISION; i++) {
            if (i % 2 == 0)
                sum += Math.pow(rad, 2*i+1) / factorial(2 * i + 1);
            else
                sum -= Math.pow(rad, 2*i+1) / factorial(2 * i + 1);
        }
        return sum;
    }

    public static void main(String []args){
        System.out.println(sin(180));
        System.out.println(Math.sin(Math.PI));

        System.out.println(sin(90));
        System.out.println(Math.sin(Math.PI/2));

        System.out.println(sin(200));
        System.out.println(Math.sin(200*2*Math.PI/360));
    }
}

Surely you can cache the values but these methods are likely to be already optimized.